Question: Solve for $x$ : $x^2 - 8x + 7 = 0$
Solution: The coefficient on the $x$ term is $-8$ and the constant term is $7$ , so we need to find two numbers that add up to $-8$ and multiply to $7$ The two numbers $-7$ and $-1$ satisfy both conditions: $ {-7} + {-1} = {-8} $ $ {-7} \times {-1} = {7} $ $(x {-7}) (x {-1}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -7) (x -1) = 0$ $x - 7 = 0$ or $x - 1 = 0$ Thus, $x = 7$ and $x = 1$ are the solutions.